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An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms

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  • Frederik Herzberg

    ()
    (Institute of Mathematical Economics, Bielefeld University)

Abstract

This paper continues Dietrich and List's [2010] work on propositional-attitude aggregation theory, which is a generalised unification of the judgment-aggregation and probabilistic opinion-pooling literatures. We first propose an algebraic framework for an analysis of (many-valued) propositional-attitude aggregation problems. Then we shall show that systematic propositional-attitude aggregators can be viewed as homomorphisms in the category of C.C. Chang's [1958] MV-algebras. Since the 2-element Boolean algebra as well as the real unit interval can be endowed with an MV-algebra structure, we obtain as natural corollaries two famous theorems: Arrow's theorem for judgment aggregation as well as McConway's [1981] characterisation of linear opinion pools.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-445.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 445.

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Length: 12 pages
Date of creation: Mar 2011
Date of revision:
Handle: RePEc:bie:wpaper:445

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Related research

Keywords: propositional attitude aggregation; judgment aggregation; linear opinion pooling; Arrow's impossibility theorem; many-valued logic; MV-algebra; homomorphism; Arrow's impossibility theorem; functional equation;

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